still kind of shaky on this I tried multiplying everything by ln so I could reduce the with the ln rule, but everything gets kind of messy and I end up getting a function that could never give me

The limit >is< meant to be x --> 0. so l'Hospital's Rule can be used.

To get the derivative of :

.

So the limit becomes:

.

Now show that .

Multiple applications of l'Hospital's rule is one possible approach.
Another approach is to substitute the series expansion for ln (1 + x): . This substitution is valid since the series converges for and ......